0123_0231_3102
Counting sequence:
1, 1, 2, 6, 21, 72, 228, 678, 1929, 5307, 14203, 37133, 95179, 239942, 596587, 1466529, 3571386, 8630575, 20725008, 49509197, 117762285, 279109649, 659555800, 1554707004, 3657127140, 8587557316, 20135214390, 47151860695, 110301150860, 257791861488, 602039016561, 1405062271696, 3277356286933, 7640894684296, 17806856523764, 41483782118066, 96613819341117, 224951333116571, 523651308515131, 1218747410245265, 2836055610154199, 6598652645316598, 15351252779728987, 35709825966595941, 83060259601647086, 193181648883727327, 449272791879254088, 1044792414401794313, 2429567462190608689, 5649498657367862497, 13136370077565296608, 30544113611033462768, 71017965797103497864, 165119773170341046252, 383902967374914511702, 892558253275295339259, 2075130461634659472096, 4824461572504825795960, 11216249501073501611993, 26076090726951609165812, 60622504565424843818865, 140936121371869203147784, 327648524968558308770060, 761713995241058920476214, 1770817374185324461439305, 4116745291097204082134771, 9570460388271602705273075, 22248998493024885336887405, 51723401066066976531491195, 120243828745299405325987678, 279536006886542435653530691, 649848412814602047645164481, 1510726350575033826566369018, 3512036827300466119288153031, 8164543382201985350830634104, 18980357219852162837391641821, 44124170476997194323623467277, 102576637882577663434563499881, 238462524931767606069129270816, 554359659543498368812475117180, 1288732946722244924034914840004, 2995946806156920373151295624908, 6964743704860599105401279615022, 16191089489571860424345660372151, 37639765946314621296204716886476, 87501938726987377866962111959032, 203417526102558022876098571196473, 472888771449320477077128228051248, 1099333810168445849119253700957349, 2555642632306480787625811316896512, 5941151485226323484808470979354588, 13811507875623359414477876415172178, 32107873037501721433812163428706349, 74641774344040387702028538090483587, 173521123827852317142417823145511267, 403387773823200372435965875322718689, 937763004138381820683005155050611831, 2180034900557486934235330812224270270, 5067967091140677333607606551045676003, 11781595724288999552698480282048773877, 27388890386830250124442192752905818270
Generating function in Maple syntax:
(x^10-6*x^9+9*x^8+9*x^7-54*x^6+94*x^5-104*x^4+76*x^3-35*x^2+9*x-1)/(2*x-1)/(x^3-2*x^2+3*x-1)/(-1+x)^5
Generating function in latex syntax:
\frac{x^{10}-6 x^{9}+9 x^{8}+9 x^{7}-54 x^{6}+94 x^{5}-104 x^{4}+76 x^{3}-35 x^{2}+9 x -1}{\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(-1+x \right)^{5}}
Generating function in sympy syntax:
(x**10 - 6*x**9 + 9*x**8 + 9*x**7 - 54*x**6 + 94*x**5 - 104*x**4 + 76*x**3 - 35*x**2 + 9*x - 1)/((x - 1)**5*(2*x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^3-2*x^2+3*x-1)*(-1+x)^5*F(x)+x^10-6*x^9+9*x^8+9*x^7-54*x^6+94*x^5-104*x^4+76*x^3-35*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(-1+x \right)^{5} F \! \left(x \right)+x^{10}-6 x^{9}+9 x^{8}+9 x^{7}-54 x^{6}+94 x^{5}-104 x^{4}+76 x^{3}-35 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/13800*(-1909*((I-107/1909*23^(1/2))*3^(1/2)-321/1909*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+18400+115*((I-91/23*23^(1/2))*3^(1/2)+273/23*I*23^(1/2)-1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(11/600*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*(-115*((I+91/23*23^(1/2))*3^(1/2)+273/23*I*23^(1/2)+1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)+18400+1909*2^(1/3)*((I+107/1909*23^(1/2))*3^(1/2)-321/1909*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*((910*2^(2/3)*23^(1/2)*3^(1/2)+230*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+18400+(-214*23^(1/2)*3^(1/2)*2^(1/3)+3818*2^(1/3))*(11+3*23^(1/2)*3^(1/2))^(2/3))*(1/300*2^(1/3)*(3*23^(1/2)*3^(1/2)-11)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/6*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/12*n^4+1/6*n^3+17/12*n^2+16/3*n-63/4*2^n+12)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-1909 \left(\left(\mathrm{I}-\frac{107 \sqrt{23}}{1909}\right) \sqrt{3}-\frac{321 \,\mathrm{I} \sqrt{23}}{1909}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+18400+115 \left(\left(\mathrm{I}-\frac{91 \sqrt{23}}{23}\right) \sqrt{3}+\frac{273 \,\mathrm{I} \sqrt{23}}{23}-1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{11 \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}-\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(-115 \left(\left(\mathrm{I}+\frac{91 \sqrt{23}}{23}\right) \sqrt{3}+\frac{273 \,\mathrm{I} \sqrt{23}}{23}+1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+18400+1909 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{107 \sqrt{23}}{1909}\right) \sqrt{3}-\frac{321 \,\mathrm{I} \sqrt{23}}{1909}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}+\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(\left(910 \,2^{\frac{2}{3}} \sqrt{23}\, \sqrt{3}+230 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+18400+\left(-214 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+3818 \,2^{\frac{1}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(3 \sqrt{23}\, \sqrt{3}-11\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{300}-\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{13800}\\+\frac{n^{4}}{12}+\frac{n^{3}}{6}+\frac{17 n^{2}}{12}+\frac{16 n}{3}-\frac{63 \,2^{n}}{4}+12 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 72
a(6) = 228
a(7) = 678
a(8) = 1929
a(9) = 5307
a(10) = 14203
a(n+4) = 1/12*n^4+1/6*n^3+5/12*n^2-2*a(n)+5*a(n+1)-8*a(n+2)+5*a(n+3)+1/3*n+5, n >= 11
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 72
a \! \left(6\right) = 228
a \! \left(7\right) = 678
a \! \left(8\right) = 1929
a \! \left(9\right) = 5307
a \! \left(10\right) = 14203
a \! \left(n +4\right) = \frac{n^{4}}{12}+\frac{n^{3}}{6}+\frac{5 n^{2}}{12}-2 a \! \left(n \right)+5 a \! \left(n +1\right)-8 a \! \left(n +2\right)+5 a \! \left(n +3\right)+\frac{n}{3}+5, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14646/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[23,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[11,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]+F[36,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[14,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[24,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[32,x]*F[4,x]
F[35,x] = F[29,x]
F[36,x] = F[118,x]+F[37,x]+F[38,x]
F[37,x] = 0
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[62,x]
F[40,x] = F[41,x]+F[7,x]
F[41,x] = F[37,x]+F[42,x]+F[49,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[48,x]
F[44,x] = F[11,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[11,x]+F[45,x]
F[48,x] = F[18,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[13,x]+F[51,x]
F[51,x] = F[52,x]+F[58,x]
F[52,x] = F[37,x]+F[53,x]+F[55,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[44,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[17,x]+F[57,x]
F[57,x] = F[52,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[22,x]+F[61,x]
F[61,x] = F[58,x]
F[62,x] = F[36,x]+F[63,x]
F[63,x] = 2*F[37,x]+F[106,x]+F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[100,x]+F[66,x]
F[66,x] = F[67,x]+F[96,x]
F[67,x] = F[37,x]+F[68,x]+F[86,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[75,x]
F[70,x] = F[11,x]+F[71,x]
F[71,x] = F[37,x]+F[42,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[14,x]+F[74,x]
F[74,x] = F[37,x]+F[53,x]+F[72,x]
F[75,x] = F[67,x]+F[76,x]
F[76,x] = 2*F[37,x]+F[64,x]+F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[29,x]+F[79,x]
F[79,x] = 2*F[37,x]+F[77,x]+F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[33,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[33,x]+F[83,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[24,x]+F[88,x]
F[88,x] = F[37,x]+F[86,x]+F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[11,x]+F[74,x]
F[92,x] = F[33,x]+F[93,x]
F[93,x] = 2*F[37,x]+F[80,x]+F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[29,x]+F[93,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[33,x]+F[99,x]
F[99,x] = F[97,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[67,x]
F[105,x] = F[101,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[101,x]+F[29,x]
F[109,x] = F[110,x]+F[114,x]
F[110,x] = 2*F[37,x]+F[111,x]+F[80,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[35,x]
F[113,x] = F[110,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[105,x]+F[117,x]
F[117,x] = F[114,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[24,x]+F[67,x]
F[121,x] = F[122,x]+F[134,x]
F[122,x] = F[123,x]+F[131,x]+F[37,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[14,x]+F[52,x]
F[126,x] = F[127,x]+F[29,x]
F[127,x] = 2*F[37,x]+F[128,x]+F[80,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[35,x]
F[130,x] = F[127,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[32,x]
F[133,x] = F[122,x]
F[134,x] = 2*F[37,x]+F[135,x]+F[144,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[139,x]
F[137,x] = F[138,x]+F[18,x]
F[138,x] = F[59,x]
F[139,x] = F[101,x]+F[140,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[105,x]+F[143,x]
F[143,x] = F[141,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[104,x]+F[146,x]
F[146,x] = F[134,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{23}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{118}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = 0
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{62}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{52}\! \left(x \right) = F_{37}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{44}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{17}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = F_{36}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{106}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{100}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{96}\! \left(x \right)
F_{67}\! \left(x \right) = F_{37}\! \left(x \right)+F_{68}\! \left(x \right)+F_{86}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{37}\! \left(x \right)+F_{53}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{67}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{64}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{29}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{33}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{33}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{24}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{37}\! \left(x \right)+F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{11}\! \left(x \right)+F_{74}\! \left(x \right)
F_{92}\! \left(x \right) = F_{33}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{80}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{29}\! \left(x \right)+F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{33}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{67}\! \left(x \right)
F_{105}\! \left(x \right) = F_{101}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{101}\! \left(x \right)+F_{29}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{110}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{111}\! \left(x \right)+F_{80}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{35}\! \left(x \right)
F_{113}\! \left(x \right) = F_{110}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{105}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{114}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{24}\! \left(x \right)+F_{67}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{134}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{131}\! \left(x \right)+F_{37}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{14}\! \left(x \right)+F_{52}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{29}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{128}\! \left(x \right)+F_{80}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{35}\! \left(x \right)
F_{130}\! \left(x \right) = F_{127}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{32}\! \left(x \right)
F_{133}\! \left(x \right) = F_{122}\! \left(x \right)
F_{134}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{135}\! \left(x \right)+F_{144}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{139}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{18}\! \left(x \right)
F_{138}\! \left(x \right) = F_{59}\! \left(x \right)
F_{139}\! \left(x \right) = F_{101}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{105}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{141}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{104}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{134}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_23(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_11(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x) + F_36(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_14(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_24(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_32(x)*F_4(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_118(x) + F_37(x) + F_38(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_62(x))
Eq(F_40(x), F_41(x) + F_7(x))
Eq(F_41(x), F_37(x) + F_42(x) + F_49(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_48(x))
Eq(F_44(x), F_11(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_11(x) + F_45(x))
Eq(F_48(x), F_18(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_13(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_58(x))
Eq(F_52(x), F_37(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_44(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_17(x) + F_57(x))
Eq(F_57(x), F_52(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_22(x) + F_61(x))
Eq(F_61(x), F_58(x))
Eq(F_62(x), F_36(x) + F_63(x))
Eq(F_63(x), F_106(x) + 2*F_37(x) + F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_100(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_96(x))
Eq(F_67(x), F_37(x) + F_68(x) + F_86(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_75(x))
Eq(F_70(x), F_11(x) + F_71(x))
Eq(F_71(x), F_37(x) + F_42(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_14(x) + F_74(x))
Eq(F_74(x), F_37(x) + F_53(x) + F_72(x))
Eq(F_75(x), F_67(x) + F_76(x))
Eq(F_76(x), 2*F_37(x) + F_64(x) + F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_29(x) + F_79(x))
Eq(F_79(x), 2*F_37(x) + F_77(x) + F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_33(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_33(x) + F_83(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_24(x) + F_88(x))
Eq(F_88(x), F_37(x) + F_86(x) + F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_11(x) + F_74(x))
Eq(F_92(x), F_33(x) + F_93(x))
Eq(F_93(x), 2*F_37(x) + F_80(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_29(x) + F_93(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_33(x) + F_99(x))
Eq(F_99(x), F_97(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_67(x))
Eq(F_105(x), F_101(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_101(x) + F_29(x))
Eq(F_109(x), F_110(x) + F_114(x))
Eq(F_110(x), F_111(x) + 2*F_37(x) + F_80(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_35(x))
Eq(F_113(x), F_110(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_105(x) + F_117(x))
Eq(F_117(x), F_114(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_24(x) + F_67(x))
Eq(F_121(x), F_122(x) + F_134(x))
Eq(F_122(x), F_123(x) + F_131(x) + F_37(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_14(x) + F_52(x))
Eq(F_126(x), F_127(x) + F_29(x))
Eq(F_127(x), F_128(x) + 2*F_37(x) + F_80(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_35(x))
Eq(F_130(x), F_127(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_32(x))
Eq(F_133(x), F_122(x))
Eq(F_134(x), F_135(x) + F_144(x) + 2*F_37(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_139(x))
Eq(F_137(x), F_138(x) + F_18(x))
Eq(F_138(x), F_59(x))
Eq(F_139(x), F_101(x) + F_140(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_105(x) + F_143(x))
Eq(F_143(x), F_141(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_104(x) + F_146(x))
Eq(F_146(x), F_134(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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